Phonon Fit for LESCO 0.125 (1-phonon model)

Generated on: 2025-07-22 11:59:01

Model Description (LaTeX)

Model description

The model is a sum of a pseudo-Voigt elastic peak (free mixing and FWHM), a Gaussian breathing phonon (free FWHM), a resolution-convolved DHO magnon, and a linear background:

Individual Components

1. Elastic Peak (Pseudo-Voigt, free mixing and FWHM)

where $\mu$ is the mixing parameter (free), $\text{FWHM}_1$ is free, and: - $L(E, x_1, \text{FWHM}_1) = \frac{(\text{FWHM}_1/2)^2}{(E - x_1)^2 + (\text{FWHM}_1/2)^2}$ (Lorentzian) - $G(E, x_1, \text{FWHM}_1) = \exp\left(-\frac{(E - x_1)^2}{2\sigma_1^2}\right)$ where $\sigma_1 = \frac{\text{FWHM}_1}{2\sqrt{2\ln(2)}}$ (Gaussian)

2. Breathing Mode (Gaussian, free FWHM)

where $\sigma_2 = \frac{\text{FWHM}_2}{2\sqrt{2\ln(2)}}$ and $\text{FWHM}_2$ is free

3. Magnon Peak (DHO convolved with fixed Gaussian resolution)

where $\gamma = \frac{FWHM_3}{2}$ (free parameter), and $G_{\text{res}}(E)$ is a Gaussian with FWHM = 0.044 eV (fixed resolution)

4. Linear Background

Fixed Parameters

  • Magnon convolution resolution: FWHM = 0.044 eV

Free Parameters

  • Elastic peak position: $x_1$
  • Elastic peak amplitude: $A_1$
  • Elastic peak FWHM: $\text{FWHM}_1$
  • Elastic mixing parameter: $\mu$
  • Breathing peak position: $x_2$
  • Breathing peak amplitude: $A_2$
  • Breathing peak FWHM: $\text{FWHM}_2$
  • Magnon peak position: $x_3$
  • Magnon peak amplitude: $A_3$
  • Magnon FWHM: $\text{FWHM}_3$
  • Background slope: slope
  • Total: 11 free parameters

Parameters and Bounds

Parameter Value
x0_1 (elastic center) [-0.100, 0.100] eV
A_1 (elastic amplitude) [0, 10]
res_1 (elastic FWHM) [0.040, 0.053] eV
mu (elastic mixing) [0.00, 1.00]
x0_2 (breathing center) [0.050, 0.200] eV
A_2 (breathing amplitude) [0, 10]
res_2 (breathing FWHM) [0.040, 0.053] eV
x0_3 (magnon center) [0.040, 0.550] eV
A_3 (magnon amplitude) [0, inf]
res_3 (magnon FWHM) [0.044, 10.000] eV
slope (background) [-1, 1]

Figures for T = 15 K (1-phonon model)

Figures

The fit results (1-phonon model)

The fit results (1-phonon model)

The phonon dispersion and FWHM (1-phonon model)

The phonon dispersion and FWHM (1-phonon model)

Phonon intensities (1-phonon model)

Phonon intensities (1-phonon model)

Figures for T = 100 K (1-phonon model)

Figures

The fit results (1-phonon model)

The fit results (1-phonon model)

The phonon dispersion and FWHM (1-phonon model)

The phonon dispersion and FWHM (1-phonon model)

Phonon intensities (1-phonon model)

Phonon intensities (1-phonon model)

Figures for T = 150 K (1-phonon model)

Figures

The fit results (1-phonon model)

The fit results (1-phonon model)

The phonon dispersion and FWHM (1-phonon model)

The phonon dispersion and FWHM (1-phonon model)

Phonon intensities (1-phonon model)

Phonon intensities (1-phonon model)

Figures for T = 200 K (1-phonon model)

Figures

The fit results (1-phonon model)

The fit results (1-phonon model)

The phonon dispersion and FWHM (1-phonon model)

The phonon dispersion and FWHM (1-phonon model)

Phonon intensities (1-phonon model)

Phonon intensities (1-phonon model)

Temperature Dependence Comparison (1-phonon model)

This section compares the temperature dependence of the elastic intensity, breathing intensity, breathing dispersion, and breathing FWHM for LESCO 0.125 (1-phonon model).

  • Colors: 15K (blue), 100K (cyan), 150K (gold), 200K (red)
  • Circles: Breathing mode; Triangles: Elastic (divided by 1.5)

Figures